The answer offered by Russell is, in case of 'identity', we substitute one with the other and vice versa. If 'a' is identical with 'b', then whatever is true for one is true for the other. Thus the truth-value of 'Fa' is same as of 'Fb'. "The author of Waverley" is in the predicate side of the sentence, which contains the description of the subject. Thus, we can frame it as "Mr. Scott is Mr. Scott", which is different from "Mr. Scott is the author of Waverley". The difference is, "Mr. Scott is the author of Waverley" is a fact in literary history, whereas the sentence "Mr. Scott is Mr. Scott" is a trivial truism.

The puzzle involved in relation to the law of identity is this. On the one hand, we cannot violate the law of identity and accept that if a = b then Fa = Fb. On the other hand, if we accept it and, thereby, accept the equivalence between 'George the IV wished to know whether Mr. Scott is the author of Waverley' and 'George the IV wished to know whether Mr. Scott is Mr. Scott', then, we find that even if the former is true, the latter is false. Here, again, one may employ the distinction between names and descriptions in order to solve the puzzle. That is, one may argue that the substitution of a for b is valid when a and b are names, not in the context where a is a name and b is a description.

There is another way in which the puzzle can be solved. This requires us to distinguish 'primary occurrence' from 'secondary occurrence' of a denoting phrase. According to Russell, if a denoting phrase D occurs in a sentence S₁ and S₁ is a part of a sentence S, then, D has a secondary occurrence; if D is in S₁ and S₁ is not a part of any sentence, then D has a primary occurrence. For example, 'the present king of France' has a primary occurrence in 'the present king of France is wise' whereas it has a secondary occurrence in 'it is not the case that the present king of France is wise'. If we do not make this distinction and follow the Russellian analysis of sentences containing definite descriptions, then, 'the present king of France is not wise' will turn out to be false as much as 'the present king of France is wise', thereby, it will lead to an absurdity of saying that two contradicting propositions can have the same truth value. A correct analysis of 'the present king of France is not wise' requires us to paraphrase it to 'it is not the case that the present king of France is wise' and once we know the truth value 'the present king of France is wise' to be false, we know that 'it is not the case that the present king of France is wise' is true.

Now, even if we know that the truth value of 'Scott is the author of Waverley' is true, the truth value of this sentence does not determine the truth value of 'George the IV wished to know whether Scott is the author of Waverley'; it is determined by the fact whether George the IV really wished to know it or not. If 'yes', it is true, if 'no', it is false. That is why, even if 'George the IV wished to know whether Scott is the author of Waverley' is true, 'George the IV wished to know whether Scott is Scott' is false.